Principal: Mr. Madison, what you've just said is one of the most insanely idiotic things I have ever heard. At no point in your rambling, incoherent response were you even close to anything that could be considered a rational thought. Everyone in this room is now dumber for having listened to it. I award you no points, and may God have mercy on your soul.
Billy(after Ms. Lippy finishes the story): Whoa whoa whoa, Ms. Lippy. The only part of the story I didn't like is that the little boy gave up looking for Happy after only an hour. He didn't put up posters or anything. He just sat on the porch like a goon and waited. That little boy's got to think; you've got a pet. You've got a responsibility. When your puppy is lost, you don't just look for an hour and then call it quits. You get your ass out there and you find that fucking dog! Ms. Lippy(dumbstruck): I... think it's time to play dodgeball.
All while the kids are sleeping.
The cursive writing scene. Billy writes a couple of words and thinks he's pretty hot shit compared to the (other) kids in his class, but then he is tasked in writing a words with "z"s in it. His suffering as he attempts to improvize/recollect what a z looks like in cursive looks pretty real.
Billy: That's not fair; Rizzuto isn't a word, he's a baseball player! You're cheating!
Billy: <sulking> I hate cursive and I hate all of you! I'm never coming back to school, NEVER!! <runs>
From the Deleted Scenes: "I'm Horny!"
The ending where everyone, even the periphery characters like the disgusting lunch lady, the bus driver, and the not so imaginary penguin all start kissing each other.
The dodgeball scene.
Billy: Now you're all in big, big trouble.
Billy's confrontation with the older O'Doyle kid:
[Threatening] O'Doyle, O'Doyle, I got a feeling your whole family is goin' down ... [Cheerfully] but right now, I gotta study!
"BILLY PASSED THE THIRD GRADE! OH WHAT A GLORIOUS DAY-AY! OH, PASSED THE THIRD GRADE! THE BILLY MADISON WAY-AY!"
The bus driver played by Chris Farley going on about how hot Veronica Vaughn is. Adam Sandler is visibly struggling to not laugh.
Bus Driver: That Veronica Vaughn is one piece of ace. I know from experience, dude. You know what I mean?
Billy: No, you don't...
Bus Driver: No, not me personally, but a guy I know, him and her Got. It. On. WOO-WEE! (laughing)
Billy: No, they didn't.
Bus Driver: No, no they didn't. But you can imagine what it'd be like if they did, right? (nudging) Huh, huh?
(Billy pats his shoulder and boards the bus)
Billy's reaction to a classmate having peed his pants, a loud-as-possible "GOO!!!"
"If peeing your pants is cool, consider me Miles Davis."
Billy visits his 3rd grade friends after getting bullied at high school. When one chubby kid says he can't wait for high school, Billy says this:
Don't you say that. Don't you ever say that. Stay here. Stay here as long as you can. (Grabs kid by the face and shakes him violently) For the love of God, cherish it. You have to cherish it.